Precalc math question help?

Question

I was wondering if anyone could help me with either, or both of these questions.

I'm a bit confused, so an explanation would be greatly appreciated :]

1. Solve for x:

x=m/n (x) + 2

2. |4-3x| is less than or equal to 7

thanks!

Answer 1

1) x=(m/n)x + 2

Get all "x" terms on one side by subtracting (m/n)x from both sides:

(1-m/n)x=2

Divide both sides by (1-m/n) to isolate x:

x=2/(1-m/n)

2) |4-3x| ≤ 7

Because of the absolute value symbol, we know that whatever is inside it can be either positive or negative, correct? So what that inequality really means is:

-(4-3x)≤7  OR  4-3x≤7

Now just solve both as you normally would solve an inequality, remembering that multiplying or dividing by a negative number turns the sign (less than/greater than) around. So for the first:

-(4-3x) ≤ 7

3x-4 ≤ 7

3x ≤ 11

x ≤ 11/3

For the second:

4-3x ≤ 7

-3x ≤ 3

x ≥ -1

So the answer is x≥-1 or x≤11/3. In interval notation, this would be written as:

x ϵ [-1,11/3]

-IMP ;) :)